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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniform stability of resolvent families
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by Carlos Lizama and Vicente Vergara PDF
Proc. Amer. Math. Soc. 132 (2004), 175-181 Request permission

Abstract:

In this article we study uniform stability of resolvent families associated to an integral equation of convolution type. We give sufficient conditions for the uniform stability of the resolvent family in Hilbert and Banach spaces. Our main result can be viewed as a substantial generalization of the Gearhart-Greiner-Prüss characterization of exponential stability for strongly continuous semigroups.
References
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Additional Information
  • Carlos Lizama
  • Affiliation: Departamento de Matemática, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile
  • MR Author ID: 114975
  • Email: clizama@usach.cl
  • Vicente Vergara
  • Affiliation: Departamento de Matemática, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile
  • Email: vvergara@usach.cl
  • Received by editor(s): August 7, 2001
  • Received by editor(s) in revised form: September 5, 2002
  • Published electronically: June 3, 2003
  • Additional Notes: The authors were supported in part by FONDECYT Grant #1010675
    This work is part of the M.Sc. thesis for the second author
  • Communicated by: Joseph A. Ball
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 175-181
  • MSC (2000): Primary 45D05, 45N05; Secondary 47D06
  • DOI: https://doi.org/10.1090/S0002-9939-03-07073-4
  • MathSciNet review: 2021260